The bonds in metal organic networks on surfaces govern the resulting geometry as well as the electronic properties. Here, we study the nature of these bonds by forming phenazine-copper complexes on a copper surface by means of atomic manipulation. The structures are characterized by a combination of scanning probe microscopy and density functional theory calculations. We observed an increase of the molecule-substrate distance upon covalent bond formation and an out-of-plane geometry that is in direct contradiction with the common expectation that these networks are steered by coordination bonds. Instead, we find that a complex energy balance of hybridization with the substrate, inhomogeneous Pauli repulsion, and elastic deformation drives the phenazine-copper interaction. Most remarkably, this attractive interaction is not driven by electron acceptor properties of copper but is of completely different donation/back-donation mechanism between molecular π-like orbitals and sp-like metal states. Our findings show that the nature of bonds between constituents adsorbed on surfaces does not have to follow the common categories.